Global Positioning System Reference
In-Depth Information
and normalized baseband signal
s
(
t
)
=
s
L
1
−
I
(
t
)
+
js
L
1
−
Q
(
t
).
(3.6)
3.2.2 Coherent Adaptive Subcarrier Modulation
The three channel signals
e
A
(
)
,
e
B
(
)
,and
e
C
(
)
of the L1 OS signal are multi-
plexed using coherent adaptive subcarrier modulation (CASM), (see Figure 3.1),
which is a multichannel modulation scheme also known as tricode hexaphase
modulation (or interplex modulation).
CASM is used to ensure that the signal transmitted from the satellite has a
constant power envelope, i.e., the total transmitted power does not vary over time.
Thus, the transmitted information is not contained in the signal amplitude and
the transmitted signal amplitude becomes less critical. This is a very desirable
property of the signal since it allows the use of efficient “class C”-like power
amplifiers.
t
t
t
The L1 OS data and pilot signals are modulated onto the carrier in-phase compo-
nent while the L1 PRS signal is modulated onto the quadrature component. The
combined signal is
)
=
α
)
cos
)
−
β
)
sin
S
(
t
e
B
(
t
)
−
α
e
C
(
t
(
2
π
f
1
t
e
A
(
t
)
+
γ
e
A
(
t
)
e
B
(
t
)
e
C
(
t
(
2
π
).
(3.7)
f
1
t
In this expression
are amplification factors that determine the distri-
bution of useful power among the channels
A
,
B
,and
C
. We assume
B
and
C
have equal power.
For
given
relative signal powers we want to solve for these variables. So let us
assume a relative signal power of 50% for
A
, and 25% for both
B
and
C
.
The first condition expresses that the norm of the
I
and the
Q
part of the sig-
nal
S
must be unity:
α
,
β
,and
γ
2
2
(α
−
α)
+
(β
+
γ)
=
1
.
The condition of equal power for both
I
and
Q
channels leads to
2
2
2
α
+
α
=
β
.
Finally, the condition that the combined power equals one leads to
2
2
2
2
α
+
α
+
β
+
γ
=
1
.
In total, we have three equations in three unknowns:
β
+
γ
=
,
1
2
2
2
α
=
β
,
2
2
2
2
α
+
β
+
γ
=
1
.
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